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<p>The <b>Davies equation</b> is an empirical equation appropiate
for ionic strengths up to <nobr>&asymp;0.1 M:</nobr>
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>log &#947;<sub><i>i</i></sub><font size="+2"> </font>= </nobr></td>
	<td valign="top"><nobr>&#8722;0.5<font size="+2"> </font><i>Z<sub>i</sub></i><sup>2</sup></nobr>
	<nobr><font size="+2">(</font>&#8730;<b><i>I</i></b> &nbsp;/
		<font size="+1">&nbsp;(</font>1+&#8730;<b><i>I</i></b>
		<font size="-2"> </font>
		<font size="+1">) &#8722;&nbsp;0.3 <b><i>I</i></b></font>
		<font size="+2">)</font></nobr>
</td></tr></table></p>

<p class="cont">
where <b><i>I</i></b> is the <a href="SP_Ionic_Strength.htm">ionic strength</a>;
<nobr>&#947;<sub><i>i</i></sub></nobr> is the
<a href="SP_Ionic_Strength.htm#Act_Coef">activity coefficient</a> of an
ion &#147;<i>i</i>&#148; with electric charge <nobr><i>Z<sub>i</sub></i>.&nbsp;</nobr>
The last parameter was initially <nobr>&#147;0.2&#148;</nobr> 
(Davies, C.W. (1938) <i><nobr>J. Chem.</nobr> Soc.</i>, 2093-<nobr>2098),&nbsp;</nobr>
but later Davies changed it to <nobr>&#147;0.3&#148;</nobr> (Davies, C.W. (1962) <i>Ion Association.</i>
London: Butterworths. <nobr>p.41).</nobr>
</p>

<p>
The <b>Davies equation</b> is derived from the
<a href="SP_Ionic_Strength_DH.htm">Debye-H&uuml;ckel <nobr>model</a>,</nobr>
simplified by setting <nobr><i>&aring;B<sub>&#947;</sub></i></nobr> =&nbsp;1
for all electrolytes, and extended with the empirical term:
<nobr>+0.15<font size="-2">&nbsp;</font><i>Z<sub>i</sub></i><sup>2</sup><font size="-2">&nbsp;</font><i><b>I</b></i>.</nobr>
</p>

<p>In <a href="S_0_Main.htm">SPANA</a>
(and <nobr><a href="SP_0_Main.htm">SED/PREDOM</a>)</nobr> the parameter
<nobr>&#147;0.5&#148;</nobr> is replaced by the temperature-dependent
solvent parameter <nobr>&#147;<i>A</i>&#148;</nobr> of the 
<a href="SP_Ionic_Strength_DH.htm">Debye-H&uuml;ckel<nobr> model</a>
<nobr>(<i>A</i>=0.509</nobr> at <nobr>25&deg;C);</nobr>
but the value <nobr>&#147;0.3&#148;</nobr> in the last term of the equation
is kept temperature-independent.
</p>

<p>The activity of water <nobr>(H<sub>2</sub>O) is given by:</nobr>
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>log <i>a</i><sub>H<sub>2</sub>O</sub><font size="+1"> </font>= </nobr></td>
	<td valign="top"><nobr>&#8722; &Phi; &#8721;<i>m<sub>k</sub></i>&nbsp;/</nobr>
		<nobr><font size="+1">(</font>ln(10)&nbsp;55.508<font size="+1">)</font></nobr>
</td></tr></table></p>

<p class="cont">
where &#147;<i>k</i>&#148; are all solute species in the aqeuous solution, and &#147;&Phi;&#148;
is the osmotic coefficient, which for the <b>Davies equation</b> it is given by:
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>&Phi;<font size="+1"> </font>= </nobr></td>
	<td valign="top">1 &#8722; <nobr>(2/3)</nobr> <nobr><font size="+1">(</font>ln(10)/&#8721;<i>m<sub>k</sub></i><font size="+1">)</font></nobr>
		<nobr><i>A</i>&nbsp;<b><i>I</i></b><sup>3/2</sup></nobr>
		<nobr><i>&sigma;</i>(&#8730;<b><i>I</i></b>)</nobr>
          <nobr>+&nbsp;<font size="+1">(</font>ln(10)/&#8721;<i>m<sub>k</sub></i><font size="+1">)</font>
					<i>A</i>&nbsp;0.3&nbsp;<b><i>I</i></b><sup>2</sup></nobr>
</td></tr></table></p>
<p class="cont">where
<table cellspacing="0" cellpadding="0" border="0">
<tr valign="top"><td><tt>&nbsp;&nbsp;&nbsp;</tt></td>
	<td valign="top"><nobr>&sigma;</i>(<i>x</i>)<font size="+2"> </font>= </nobr></td>
	<td valign="top"><nobr>(3/<i>x</i><sup>3</sup>)</nobr> <nobr><font size="+2">(</font>(1+<i>x</i>)</nobr> <nobr>&#8722; 1/(1+<i>x</i>)</nobr> <nobr>&#8722; 2 ln(1+<i>x</i>)<font size="+2">)</font></nobr>
</td></tr></table></p>

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